,

so 4 and 2 are not solutions, but -15 and -18 are.

  1. -1 is not included in the set, so the interval notation is B. Square brackets would indicate that a number is included.
  1. This can be rewritten as Neither -8 nor -5 are included, so the answer is B. (-8,-5)
  1. The line includes all numbers from -6 to 5, not including the endpoints because of the parentheses. The answer is C. (-6,5)
  1. . The graph for this is a square bracket at -16 with a solid line extending to infinity.
  1. Two details here. Dividing by a negative number reverses the equality sign. Also, dividing by a fraction is the same as inverting the fraction and multiplying.
  1. For the second part, So Francis has to weigh less than 200.9 pounds to be in the low-risk category.
  1. You need to know for what range of bills, , is plan B cheaper. So plan B is cheaper if her bills are more than $2000.
  1. These two sets have no elements in common, so their intersection is the empty set. Enter N.
  1. These two inequalities can be combined into This is represented by a line connecting a bracket at -6 to a parenthesis at 9. The answer is A.
  1. For the first, For the second, . These two solutions can be combined into This is represented by a line connecting a bracket at -8 to a parenthesis at 3.
  1. Break this up into two equations. , and Combining these, the solution is
  1. Same as above. and Combining these, the solution is Also note that
  1. or is represented by a parenthesis at -3 with a line extending to negative infinity, and a parenthesis at 2 with a line extending to positive infinity. The answer is A.
  1. The second is Combining these, we have or This is represented by a parenthesis at -12 with a line extending to negative infinity, and a parenthesis at -7 with a line extending to positive infinity. This looks like the graph in the previous problem with the new numbers.
  1. For the second, Combining these or
  1. Let be the number of beats in 10 seconds. There are 6 ten second intervals in a minute, so the number of beats per minute is For maximum results, and Solving for the first, and for the second Rounding, the beats in 10 sec should be between 23 and 27 beats.
  1. Simply plug the point in. This is less than , so it is a solution.
  1. The shaded area not including the line is the solution. This is sometimes represented with a dotted or dashed line since it is not included.
  1. Solve this for y. The shaded area including the line is the solution.
  1. Solve for y. The shaded area including the line is the solution.
  1. Graph 1 represents since it has a slope of m = -1 and y intercept of b = 4, and the area below is shaded. This is a rearrangement of B.
  1. Graph 1 represents since it has a slope of m = -1 and y intercept of b = -3, and the area below is shaded. This is a rearrangement of B.
  1. The cyan and dark green regions are the first equation, the peach and dark green regions are the second equation, and the dark green region satisfies both inequalities. For your graph, only include the dark green region.
  1. They leave a fun one for the end! Solve the first two equations for y. and Graphing these 4 lines and highlighting the regions represented produces the plot below. Only the darkest region in the center, which satisfies all 4 equations, represents the solution, so your graph should be only this 4-sided region.